Mr Lee Hsien Yang responded to his elder brother, Prime Minister Lee Hsien Loong, in Facebook posts yesterday, saying in one that it was "wrong to lie to Parliament and it is wrong to lie under oath".
He said a statement that PM Lee made in Parliament contradicts the statutory declarations he made to a ministerial committee .
Mr Lee Hsien Yang was referring to a statement made by PM Lee to Parliament on April 13, 2015, on the home of their father, the late Mr Lee Kuan Yew, at 38, Oxley Road.
PM Lee told the parliamentary session - held nearly a month after Mr Lee's death on March 23, 2015 - that his father was adamant that the house should be demolished after his death and not turned into a museum and a memorial to him .
Mr Lee Hsien Yang's post was also a reference to what PM Lee had stated in statutory declarations to a ministerial committee that was set up to consider options for the Oxley Road house.
The committee's existence came to light on Wednesday in a statement issued by Mr Lee Hsien Yang and his sister, Dr Lee Wei Ling, that was critical of PM Lee and which centred on the long-running dispute over the future of the Oxley Road house.
In a summary of the statutory declarations that PM Lee made to the committee, released through his lawyers yesterday, PM Lee rejected his siblings' claims that Mr Lee was not prepared to accept the preservation of the house, or other options short of demolition. "There is no basis for these claims, not least because of the deeply troubling circumstances concerning the making of the last will."
He also said later in the declarations that he held firm against objections from his brother and his wife Lee Suet Fern to him reading out in Parliament the full version of the demolition clause in the final will.
The full version included what the late Mr Lee wanted done to the house if it was not demolished - namely that the house be open only to his children, their families and their descendants.
But Mr Lee Hsien Yang said in his post last night: "We have a question for Lee Hsien Loong: Does he or does he not believe that Lee Kuan Yew was unwavering in his wish that the house be demolished? Is his statement to Parliament false, or is his statement under oath false?"
He also took aim at a point PM Lee made in the statutory declarations: that there was no evidence that their father knew that the demolition clause had been re-inserted into his last will.
To make his point, Mr Lee Hsien Yang's post included a picture of Mr Lee's initials just below the clause in the will.
"How could Lee Kuan Yew not know when he initialled right beneath the Demolition Clause, and (Lee Hsien Loong) has the will?" he added.
Earlier yesterday, Mr Lee Hsien Yang said in a separate Facebook post that the will of their late father was "final and binding". "We have no confidence in Lee Hsien Loong or his secret committee."
He also presented a series of statements to show discrepancies between statements PM Lee made in public and to the ministerial committee.
On the issue of deciding what to do with the house, for instance, he said PM Lee told Parliament "there is no immediate issue of demolition of the house, and no need for the Government to make a decision now".
But Mr Lee Hsien Yang noted that a "secret" committee of ministers was then set up to investigate and make recommendations about the house.
On the issue of Mr Lee's will, Mr Lee Hsien Yang said that probate for the will was granted on Oct 6, 2015, and that meant it was recognised as final and legally binding.
He said PM Lee raised no legal challenge at that time.
But in private, Mr Lee Hsien Yang said, PM Lee wrote to the ministerial committee to say "there is no evidence that Mr Lee even knew that the demolition clause had been re-inserted into the last will''.
He also said that on Mr Lee's position on the house, PM Lee quoted the demolition clause in Parliament and said that his father's position on the house was "unwavering over the years, and fully consistent with his lifelong values".
Mr Lee Hsien Yang added that PM Lee told the ministerial committee that "(Mr Lee Kuan Yew) then took a number of steps which put beyond any doubt that he came to accept Cabinet's position."